Problem: Simplify the following expression: $k = \dfrac{30mp + 25np}{10p^2 + 5p} - \dfrac{20p^2}{10p^2 + 5p}$ You can assume $m,n,p \neq 0$.
Explanation: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{30mp + 25np - (20p^2)}{10p^2 + 5p}$ $k = \dfrac{30mp + 25np - 20p^2}{10p^2 + 5p}$ The numerator and denominator have a common factor of $5p$, so we can simplify $k = \dfrac{6m + 5n - 4p}{2p + 1}$